ln(2x+7)-ln(x)=ln(5)

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Solution for ln(2x+7)-ln(x)=ln(5) equation: 


Simplifying
ln(2x + 7) + -1ln(x) = ln(5)

Reorder the terms:
ln(7 + 2x) + -1ln(x) = ln(5)
(7 * ln + 2x * ln) + -1ln(x) = ln(5)
(7ln + 2lnx) + -1ln(x) = ln(5)

Multiply ln * x
7ln + 2lnx + -1lnx = ln(5)

Combine like terms: 2lnx + -1lnx = 1lnx
7ln + 1lnx = ln(5)

Reorder the terms for easier multiplication:
7ln + 1lnx = 5ln

Solving
7ln + 1lnx = 5ln

Solving for variable 'l'.

Move all terms containing l to the left, all other terms to the right.

Add '-5ln' to each side of the equation.
7ln + -5ln + 1lnx = 5ln + -5ln

Combine like terms: 7ln + -5ln = 2ln
2ln + 1lnx = 5ln + -5ln

Combine like terms: 5ln + -5ln = 0
2ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(2 + x) = 0


Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve:

Simplifying
ln = 0

Solving
ln = 0

Move all terms containing l to the left, all other terms to the right.

Simplifying
ln = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

Move all terms containing l to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Add '-1x' to each side of the equation.
x + -1x = -2 + -1x

Combine like terms: x + -1x = 0
0 = -2 + -1x

Simplifying
0 = -2 + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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